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Eccentricity vector
In astrodynamics the eccentricity vector of a conic section orbit is the vector pointing towards the periapsis and with length equal to the orbit's scalar eccentricity.
Calculation
The eccentricity vector 
can be calculated from the orbital state vectors 
and 
at any time (the result is constant):
![\mathbf{e} = {1 \over {\mu}} \left [\left (v^2 - {\mu \over {\mathbf{\left |r \right |}}}\right) \mathbf{r} - (\mathbf{r} \cdot \mathbf{v} ) \mathbf{v} \right ]](a/../upload/math/36fff1942e31e17360b65327f8fb71b7.png)
where:
- is velocity vector of the orbital state vectors,
- is position vector of the orbital state vectors,
is standard gravitational parameter.
Alternatively it can also be computed from orbital angular momentum vector h:
where:
is orbital velocity vector,
is orbital angular momentum vector,
is orbital position vector,
is standard gravitational parameter.
See also
Last updated: 10-25-2005 17:49:01
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details